Due to the importance of the Regularity lemma several researchers found weakened versions ([1]}, [2]}, etc.) in which the dependence of \(\varepsilon \)  and \(n_0\)  is not determined by a tower function. These are important developments with several applications, still, none of them seems to be so widely applicable as the original one.
The so called absorption method [3]} is also a choice for avoiding the use of the Regularity lemma in some embedding problems.
